correlation analysis in agilent genespring and mass … · correlation analysis in agilent...

Correlation Analysis in Agilent

GeneSpring and Mass Profi ler

Professional“Is there a relationship between variable X and variable Y? This is a central question for

the data analyst. The answer comes from examination of the correlation between the

two.”

Chen, P; Popovich, P. “Correlation: Parametric and Nonparametric Measures”.

Sage Publications, 2002.

Technical Overview

Authors

Pritha Aggarwal, Durairaj Renu, and

Pramila Tata

Strand Life Sciences

Bangalore, India

Michael Rosenberg

Agilent Technologies, Inc.

Santa Clara, California, USA

Introduction

Correlation analysis allows identifi cation of coregulated molecules such as genes

and metabolites as well as identifi cation of relationships between the samples in a

study. Introduced in the GeneSpring/Mass Profi ler Professional (MPP) 13.0 platform,

the correlation framework is supported on most of the datasets generated using

high-throughput omics platforms such as Microarray, Mass Spectrometry, and Next

Generation Sequencing. The framework supports pair-wise correlations measured using

a single technology platform and cross-technology measurements between two different

platforms.

This Technical Overview describes the details of the correlation framework supported in

GeneSpring/MPP 13.0.

2

The Spearman correlation

coeffi cient (http://en.wikipedia.

org/wiki/Spearman’s_rank_

correlation_coeffi cient) is a

rank-based algorithm, and is more

tolerant to the outliers in datasets

than Pearson. Both Pearson and

Spearman metrics are available in

the GeneSpring/MPP Correlation

Framework.

• In biological systems, positive

correlation is observed between

transcriptional activators and their

target genes; inhibitors such as

miRNA and their mRNA targets are

negatively correlated.

• At least three data points are

required to perform correlation

analysis; by defi nition, for any two

data points correlation coeffi cient

is +1, –1, or undefi ned.

• There are many methods for

computing correlation, but

the most commonly used

are Pearson and Spearman

correlation coeffi cients. The

Pearson correlation coeffi cient

(http://en.wikipedia.org/wiki/

Pearson_product-moment_

correlation_coeffi cient) is broadly

used for fi nding the strength of

linear relationships within normally

distributed random variables.

Key Correlation Concepts

Correlation analysis is one of the most

widely used statistical techniques.

Correlation measures the strength and

directionality of the linear relationship

between two quantitative variables.

(http://en.wikipedia.org/wiki/

Correlation_and_dependence).

• When high scores of variable X

tend to accompany high scores of

variable Y, the two variables are

said to be positively correlated.

When low scores of X tend to

accompany high scores of Y,

the two variables are said to

be negatively correlated or

anticorrelated.

• Correlation values range from –1 to

+1. If two variables are positively

correlated, the value of their

correlation coeffi cient is close to

+1; then +1 itself indicates perfect

correlation. Similarly, if the two

variables are negatively correlated,

their correlation coeffi cient

approaches –1. A low correlation

coeffi cient indicates that there is

no signifi cant dependency between

the two variables.

• Correlation measures only the

degree of linear association

between two variables. It does

not imply a cause-and-effect

relationship between the variables.

• For a straightforward linear

regression, goodness of fi t equals

squared Pearson correlation

coeffi cient (R2 and R in Figure 1).

Therefore, correlation can be

thought of as a measure of

deviation of empirical data from

the linear regression fi t.

Figure 1. Pearson correlation coeffi cient (CC) between variables X and Y. The scatter plot of the empirical

data with regression line displays the positive correlation between X and Y.

3

Entity-Entity Correlation

Correlation analysis is performed in a

pair-wise manner to identify and observe

dependency between abundance levels of

any pair of biological entities. An entity in

GeneSpring/MPP is a gene, metabolite,

protein, or a probe in an expression array.

The option to perform correlation analysis

is included in the Workfl ow Browser of

the experiment. A correlation analysis

can be performed on entities within a

single experiment or across two different

Table 1. Analysis types in GeneSpring available for correlation analysis.

Analysis type Within single experiment Across two experiments

mRNA expression Yes Yes

Exon expression Yes Yes

miRNA Yes Yes

RTPCR Yes Yes

DNA-Seq No No

RNA-Seq No Yes*

smallRNA-Seq No Yes*

Metabolomics Yes Yes

Proteomics Yes Yes

* To perform correlation in RNA-Seq and smallRNA-Seq experiments, data from Strand NGS v2.1 software

(http://www.strand-ngs.com/) should be imported into GeneSpring.

Figure 2. Calculation of correlation coeffi cients between entities of a single experiment. A table of expression values is created based upon the normalized

intensities (abundance) of selected entities in a set of samples. Pair-wise correlation coeffi cients (Pearson or Spearman) are computed between each pair of

rows in the expression table and represented as a heatmap.

Entity expression values Correlation coefficients Correlation heatmap

CC

mR1mR2mR3mR4mR5mR6mR7mR8mR9mR10mR11mR12mR13mR14mR15mR16mR17mR18mR19mR20mR21mR22mR23mR24mR25

mR

1

mR

2

mR

3

mR

4

mR

5

mR

6

mR

7

mR

8

mR

9

mR

10

mR

11

mR

12

mR

13

mR

14

mR

15

mR

16

mR

17

mR

18

mR

19

mR

20

mR

21

mR

22

mR

23

mR

24

mR

25

Correlation value by color

+1 –10

experiments. For cross-experiment

correlation analysis, a Multi-Omics

Analysis (MOA) experiment should be

created in GeneSpring using the two

experiments whose entities would

be selected for correlation. Table 1

summarizes the types of GeneSpring

experiments that support correlation

analysis.

Correlation analysis on entities from

a single experiment and from two

experiments are explained in Figures 2

and 3 respectively.

Inputs for Correlation Analysis

The output of the correlation analysis

performed within a single or a MOA

experiment is determined by the entity

list, interpretation, and type of correlation

coeffi cient selected as inputs for the

analysis.

Entity list: Pair-wise correlations between

the entities in a chosen entity list(s) are

calculated. GeneSpring/MPP allows

selecting an entity list from the active

experiment, or two different entity lists

from the two experiments in a MOA

experiment.

Interpretation: As any other analysis in

GeneSpring, if averaged interpretation

is chosen, the mean intensity value for

each entity across the replicates will be

used for analysis. In the nonaveraged

interpretation, the intensity value for the

entity in each sample will be used for the

analysis.

Supported types of correlation: In

GeneSpring 13.0, the Correlation Analysis

Framework supports Pearson and

Spearman correlation coeffi cients; other

types will be added in future releases.

GeneSpring requires a minimum of

three valid data points to calculate

correlation between a pair of entities. If

a nonaveraged interpretation is used, a

minimum of three samples have to be

included as part of the interpretation. In

an averaged interpretation, a minimum of

three conditions are required.

4

cross-experiment entities, as shown in

Figure 4.

Data underlying each cell in a correlation

heatmap can be examined as a scatter

plot. A scatter plot provides a graphical

representation of the empirical

abundance values that were used to

compute the correlation coeffi cient

between a given entity pair. The

regression fi t and equation in the plot

display the direction and strength of the

dependency between the pair of entities

(Figure 5).

This applies to correlation performed

on entities of a single experiment,

or between entities of two different

experiments as in a MOA experiment.

The resulting heatmap is a square

diagram with a diagonal representing the

correlation of each entity with itself (that

is, all values on the diagonal equal +1).

A heatmap view of correlation between

entities in a single experiment or MOA

experiment are shown in Figures 2

and 3 (the right-most panels). In a MOA,

the view can be toggled between a

heatmap of all entities or a heatmap of

Correlation Heatmaps

The correlation coeffi cients for selected

datasets are visually represented as a

heatmap. A correlation heatmap is a

convenient tool for understanding the

relationship between multiple entities.

The color of each cell in the heatmap

is defi ned by the pair-wise correlation

coeffi cient value between the given entity

in the X and Y-axes of the heatmap.

The order of entities in a heatmap is

the same in both X and Y dimensions.

Concatenated expression table Correlation coefficients Correlation heatmap

CC

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CDKN1BTAF5ACTR1AAMOTL2DGKIMTSS1SATB1CHD7SOX4FAM77CDPYSL4PAK3CDK5R1CA10RP11-35N6.1DNM3HN1BAI3E2F3SPASThsa-miR-142-3phsa-miR-152hsa-miR-195hsa-miR-204hsa-miR-22hsa-miR-223hsa-miR-23ahsa-miR-26ahsa-miR-27ahsa-miR-29ahsa-miR-29bhsa-miR-29chsa-miR-30chsa-miR-34ahsa-miR-98

hsa

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-142

hsa

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hsa

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hsa

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hsa

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hsa

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hsa

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hsa

-miR

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hsa

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hsa

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hsa

-miR

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hsa

-miR

-29c

hsa

-miR

-30c

hsa

-miR

-34a

hsa

-miR

-98

Correlation

value by

color

+1

–1

0

Figure 3. Pair-wise correlation calculation between entities of two different experiments. Similarly to single experiment correlation analysis, individual tables of

expression values are created for Experiment 1 and Experiment 2. The two expression tables are concatenated based on the sample pairing information provided

by the user. For cross-experiment correlation analysis, it is expected that the same or similar biological samples are measured by the two different platforms.

If m entities are selected from Experiment 1 and n entities from Experiment 2, the concatenated heatmap will have m+n entities on each axis. The calculated

correlation coeffi cient values are represented as a heatmap.

AToggle ON

CDKN1BTAF5ACTR1AAMOTL2DGKIMTSS1SATB1CHD7SOX4FAM77CDPYSL4PAK3CDK5R1CA10RP11-35N6.1DNM3HN1BAI3E2F3SPASThsa-miR-142-3phsa-miR-152hsa-miR-195hsa-miR-204hsa-miR-22hsa-miR-223hsa-miR-23ahsa-miR-26ahsa-miR-27ahsa-miR-29ahsa-miR-29bhsa-miR-29chsa-miR-30chsa-miR-34ahsa-miR-98

CD

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Thsa

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hsa

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hsa

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hsa

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hsa

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hsa

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hsa

-miR

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hsa

-miR

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hsa

-miR

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hsa

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hsa

-miR

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hsa

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hsa

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hsa

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hsa

-miR

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BToggle OFF

CDKN1B

TAF5

ACTR1A

AMOTL2

DGKI

MTSS1

SATB1

CHD7

SOX4

FAM77C

DPYSL4

PAK3

CDK5R1

CA10

RP11-35N6.1

DNM3

HN1

BAI3

E2F3

SPAST

hsa

-miR

-142

hsa

-miR

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hsa

-miR

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hsa

-miR

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hsa

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hsa

-miR

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hsa

-miR

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hsa

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hsa

-miR

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hsa

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hsa

-miR

-29b

hsa

-miR

-29c

hsa

-miR

-30c

hsa

-miR

-34a

hsa

-miR

-98

Figure 4. MOA correlation heatmap. The view can be switched between (A) all input entities or (B) cross-experiment only using the ON/OFF toggle in the menu bar.

5

Filtering Entities in a Correlation Heatmap

The output of many statistical analyses

performed in GeneSpring/MPP is saved

as entity list-associated data, for example,

Fold change, p-value, or Regulation.

In the correlation analysis framework,

researchers can use any associated data

to fi lter the correlation heatmap. Filtering

is supported both on numerical data, such

as fold change or p-value, and categorical

data, for example, Up/Down Regulation

(Figure 6A). If more than one fi lter is

applied at a given instance, entities

passing all of the applied fi lters are

retained in the view (Boolean AND).

Correlation framework supports fi ltering

a heatmap based on any attributes

associated with entities, including

external attributes. External entity

attributes are imported into GeneSpring

by uploading an entity list with all

associated values from a tab-delimited

text or an Excel fi le. In the example

illustrated in Figure 6A, each imported

gene (Figure 6B) has a pathway it belongs

to as an associated value. Filtering

a heatmap by a pathway name (for

example, Receptor Tyrosine Kinases (RTK)

in Figure 6B) allows a user to explore

the relationship between the expression

levels of the members of the selected

pathway.

Figure 5. Example of a scatter plot showing negative correlation between the highlighted pair of entities,

including empirical data, linear regression fi t, and correlation coeffi cient.

Regressionequation

Regressionline

Correlation coefficient

CD

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1B

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77C

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E2F3

SPA

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P4H

A2

CO

L1A

1

TH

BS

1

CA

ST

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C1

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2

AN

XA

2

TG

FBI

SLC

10A

3

DS

E

DGKI

MTSS1

SATB1

CHD7

SOX4

RP11-35N6.1

DNM3

HN1

BAI3

E2F3

SPAST

P4HA2

COL1A1

THBS1

CAST

SHC1

TGOLN2

ANXA2

TGFBI

SLC10A3

DSE

A B

Numerical filter

Categorical filter

Text query filter

Heatmap was filtered to show

only members of the RTK

pathway; the pathway

information was imported from

an external file

External file format

Identifier Pathway

AKT1

BRAF

CBL

EGFR

ERBB2

ERBB3

FGFR1

FGFR2

GRB2

MET

NF1

NRAS

PDGFRA

PDGFRB

RAF1

SPRY2

BR

AF

CB

L

EG

FR

ER

BB

2

ER

BB

3

FGFR

1

FGFR

2

GR

B2

MET

NF1

NR

AS

PD

GFR

A

PD

GFR

B

RA

F1

SP

RY2

AKT

AKT2 AKT

AKT3 AKT

ARAF RKT

ATM P53

BRAF RKT

CBL P53

CCND1 P53

CCND2 RKT

CCNE1 RB

CDKN2A RB

CDKN2B RB

CDKN2C RB

E2F1 RB

EGFR RKT

EP300 P53

ERBB2 RKT

Figure 6. Numerical and categorical fi ltering. A) In this example, Fold Change (FC) is a numerical fi lter and Pathway and Genes_GBM are categorical fi lters.

If the number of different categories is less than 30, it will be displayed in the fi lter panel as checkboxes (see Categorical fi lter in the fi gure). A text box will

be displayed if the number of values exceeds 30 (see Text Query fi lter in the fi gure). B) Is an example of an external entity list with associated values used for

fi ltering.

The correlation framework allows saving

the entities that passed a fi lter or fi lters.

In the experiment navigator, the new

entity list will appear under the node

for correlation analysis where it was

generated. For example, in Figure 6,

where the heatmap was fi ltered to display

only members of the RTK pathway,

correlation between the members of this

pathway can be saved for future analysis

and reference.

In a MOA correlation, two fi ltering tabs

are provided, one for each experiment.

6

In a single experiment, clustering is

performed based on the pair-wise

correlation coeffi cients between all

entities in a given entity list. In a MOA

experiment, clustering is performed based

on cross-experiment correlation values

only (Figure 7). If a fi ltering option was

applied prior to clustering, in either a

single-technology or a MOA experiment,

clustering is performed only on those

entities that passed the fi lters. If fi ltering

is applied after clustering, the clustering

dendrogram is removed, and the order of

entities in the heatmap is reset to default.

Clustering Entities in a Correlation Heatmap

The GeneSpring/MPP Correlation

Framework allows hierarchical clustering

of entities based on their correlation

coeffi cients rather than their expression

values. It is an important functionality

because co-expressing entities are likely

to share common biological functions

and, therefore, a clustering result may

suggest a new hypothesis or confi rm

existing assumptions. The clustering

parameters supported by the correlation

framework are summarized in Table 2.

Parameter Value

Distance metric Euclidean, Squared Euclidean,

Manhattan (Cityblock),

Maximum (Chebychev),

Minimum, Differential,

Canberra, Harmonic,

Pearson’s Centered,

Pearson’s Uncentered

(Cosine), Pearson’s Centered

– Absolute, or Pearson’s

Uncentered – Absolute

Linkage rule Average, Centroid, Ward’s,

Median, Single or Complete

Table 2. Summary of parameters supported for

hierarchical clustering in GeneSpring.

exp1/exp1 CCs exp1/exp2 CCs

exp2/exp1 CCs exp2/exp2 CCs

This dendogram is based on the distance between rows in the cross-experiment quadrant only (highlighted).

This dendogram is based on the distance between columns in the cross-experiment quadrant only (highlighted).

CDKN1B

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ACTR1A

AMOTL2

DGKIMTSS1SATB1

SOX4

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DPYSL4CHD7

PAK3

CDK5R1

CA10

RP11-35N6.1

DNM3

HN1

BAI3

E2F3

SPAST

hsa-miR-142-3p

hsa-miR-152

hsa-miR-195

hsa-miR-204

hsa-miR-22hsa-miR-223

hsa-miR-23a

hsa-miR-26a

hsa-miR-27ahsa-miR-29a

hsa-miR-29bhsa-miR-29c

hsa-miR-30c

hsa-miR-34a

hsa-miR-98

CD

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p

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Figure 7. Clustering in MOA uses profi le defi ned by cross experiment correlation values.

7

Entities of interest in the correlation

heatmap can be selected and saved as an

entity list of selection. The saved entity

list can be used for further analysis in

GeneSpring as any other entity list. For

example, the entities that make up a

cluster of interest can be selected and

saved as an entity list. Performing Gene

Ontology analysis or Pathway analysis

on the saved entity list would identify

the biological function or pathway that is

enriched in the cluster of interest.

Highlighting and Selecting Entities

The correlation framework in

GeneSpring/MPP permits highlighting

the subset of entities in a correlation

heatmap that matched the selected entity

list. Entities matching the selected list are

highlighted by a red hash bar located next

to the corresponding row and column. By

default, unmatched entities are hidden

from view by setting the transparency

level to 0 (Figure 9). The transparency is

customizable and can be changed in the

heatmap property dialogue.

Exporting Correlation Coeffi cients

The correlation framework supports

exporting the correlation coeffi cients

for all, fi ltered, or selected entities. The

associated data and annotations can also

be exported (Figure 8).

Figure 8. View of an output fi le after exporting correlation coeffi cients. Along with pair-wise correlation coeffi cient values, the entity associated data and

annotations are exported both for rows and columns. The Correlation Coeffi cients are shown in peach color, the column annotations in blue, and the row

annotations in green.

Figure 9. Highlighted entities are shown with a red color hash bar, and selected entities are indicated by

a green color hash bar. The highlight and selection colors are customizable and can be changed in the

heatmap property dialogue.

Unmatched entitycorrelationdisplayed inbackground color

Selected entity

Highlighted entity

CD

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CDKN1B

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CDK5R1

BAI3

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hsa-miR-142-3p



hsa-miR-23a

hsa-miR-26a

hsa-miR-27ahsa-miR-29a

hsa-miR-29bhsa-miR-29c

hsa-miR-34a

hsa-miR-98

8

between Sample 1 and Sample 2

based on the signal intensity values of

Genes 1–12. A selected entity list and

interpretation are used to defi ne the

samples and entities for correlation

analysis.

Sample-sample correlation analysis is

sensitive to baseline transformation

performed during the experiment creation.

The biological inference derived from

the analysis will be altered by using

baseline transformed data. It is advisable

to perform sample-sample correlation

on data which has not been baseline

transformed.

The output of sample-sample correlation

is displayed as a heatmap. Samples in

the heatmap can be clustered using

hierarchical clustering based on the

correlation profi les of the samples

(Figure 10).

Sample-Sample Correlation

In addition to entity-entity correlation, the

GeneSpring/MPP Correlation Framework

supports pair-wise correlation analysis

between biological samples within a

given experiment. Sample correlation

allows identifi cation of the condition-wise

relationships that may exist between the

samples in a study.

Sample correlation is performed on the

same experiment types that are supported

for entity correlation (Table 1). Sample

correlation is supported only between the

samples in a single experiment; it is not

supported for MOA experiments.

The sample correlation analysis is defi ned

by the entity list, interpretation, and type

of correlation coeffi cient selected as

inputs for the analysis. Table 3 depicts

an example of a correlation computed

Table 3. Example calculation of correlation

between two given samples.

Sample 1 Sample 2

Gene 1 0.651 1.372

Gene 2 0.818 1.590

Gene 3 0.945 1.716

Gene 4 0.578 0.643

Gene 5 0.464 1.186

Gene 6 0.675 0.947

Gene 7 0.323 0.642

Gene 8 0.304 0.774

Gene 9 0.043 0.783

Gene 10 0.943 1.452

Gene 11 0.908 1.686

Gene 12 0.415 0.808

Pearson 0.822

Figure 10. Sample-sample correlation heatmap for a metabolomics study2. Clustering on correlation coeffi cients clearly demonstrates that samples group

together based on their pH values rather than infection status (NRBC = Noninfected RBCs, IRBC = Infected RBCs).

pH 9.0

pH 2.0

pH 7.0

Tube no. NRBCIRBC at 10 %

SLO 250stock units Set A Set B Set C

1-1 500 µL pH 2 pH 7 pH 9

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4-2 500 µL 10 µL pH 2 pH 7 pH 9

4-3 500 µL 10 µL pH 2 pH 7 pH 9

4-4 500 µL 10 µL pH 2 pH 7 pH 9

The sample-sample correlation heatmap indicates a strong relationship

within a pH as compared to Plasmodium falciparum infection status.

9

References

1. The results shown in the document

are in whole or part based upon data

generated by the TCGA Research

Network: http://cancergenome.nih.

gov/

2. Sana, T. R; et al. Global Mass

Spectrometry Based Metabolomics

Profi ling of Erythrocytes Infected

with Plasmodium falciparum. PLoS

ONE 2013, 8(4): e60840. doi:10.1371/

journal.pone.0060840.

10

Notes

11

Notes

www.agilent.com/chem

This information is subject to change without notice.

© Agilent Technologies, Inc., 2014, 2016 Published in the USA, March 17, 2016 5991-5165ENPR7000-0389

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